Minimum Cricket Matches for Fair Win Chance

XAT 2010 · Quantitative Ability & Data Interpretation · Easy · Quantitative Ability

The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?

  1. A.

    3

  2. B.

    4

  3. C.

    5

  4. D.

    6

  5. E.

    None of the above

Answer

B

Explanation

Fair chance means probability of winning at least one match ≥1/2\ge 1/2. P(winning at least 1)=1−(5/6)n≥1/2  ⟹  (5/6)n≤1/2P(\text{winning at least 1}) = 1 - (5/6)^n \ge 1/2 \implies (5/6)^n \le 1/2. For n=3n = 3: (5/6)3=125/216≈0.578>0.5(5/6)^3 = 125/216 \approx 0.578 > 0.5. For n=4n = 4: (5/6)4=625/1296≈0.482≤0.5(5/6)^4 = 625/1296 \approx 0.482 \le 0.5. Minimum matches required = 4.

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